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Harmonic Analysis on p-adic Unipotent Groups

  • Khemais Maktouf
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Abstract

Let G be a p-adic unipotent group and let H be an algebraic subgroup of G. Given a unitary character χ of H, we consider the monomial representation IndHGχ. To the character χ, we associate the affine subspace Xχ=f+h⊥⊂g* where f is a linear form associated with χ. We describe the irreducible representations occurring in the central decomposition of IndHGχ in terms of the coadjoint orbits in g* that meet Xχ. We also determine the corresponding measure class on the unitary dual Ĝ. Furthermore, we study the multiplicities of the irreducible representations in this decomposition. As an application, we compute the Plancherel formula for IndHGχ when H is a normal algebraic subgroup of G and the multiplicities are finite.

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Cite

BibTeXRIS
BibTeX
@misc{maktouf2026harmonic,
  title = {{Harmonic Analysis on $p$-adic Unipotent Groups}},
  author = {Khemais Maktouf},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40099},
  eprint = {2610.40099},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40099},
}
RIS
TY  - UNPB
TI  - Harmonic Analysis on p-adic Unipotent Groups
AU  - Khemais Maktouf
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40099
UR  - https://arxiv.org/abs/2610.40099
AB  - Let G be a p-adic unipotent group and let H be an algebraic subgroup of G. Given a unitary character χ of H, we consider the monomial representation Ind_H^Gχ. To the character χ, we associate the affine subspace X_χ=f+h^⊥⊂g^* where f is a linear form associated with χ. We describe the irreducible representations occurring in the central decomposition of Ind_H^Gχ in terms of the coadjoint orbits in g^* that meet X_χ. We also determine the corresponding measure class on the unitary dual Ĝ. Furthermore, we study the multiplicities of the irreducible representations in this decomposition. As an application, we compute the Plancherel formula for Ind_H^Gχ when H is a normal algebraic subgroup of G and the multiplicities are finite.
ER  -